6 papers · 1 filter
Three representations of the fractional -Laplacian: semigroup, extension and Balakrishnan formulas
Félix del Teso, David Gómez-Castro, Juan Luis Vázquez
We introduce three representation formulas for the fractional -Laplace operator in the whole range of parameters and . Note that for this a nonlinea…
A mean value formula for the variational -Laplacian
Félix del Teso, Erik Lindgren
We prove a new asymptotic mean value formula for the -Laplace operator, valid in the viscosity sense. In the plane, and for a c…
Characterization of nonlocal diffusion operators satisfying the Liouville theorem. Irrational numbers and subgroups of
Nathaël Alibaud, Félix del Teso, Jørgen Endal +1
We investigate the characterization of generators of Lévy processes satisfying the Liouville theorem: Bounded functions solving are constant. T…
Porous medium equation with nonlocal pressure
Diana Stan, Félix del Teso, Juan Luis Vázquez
We provide a rather complete description of the results obtained so far on the nonlinear diffusion equation , which describes a flow thr…
On distributional solutions of local and nonlocal problems of porous medium type
Félix del Teso, Jørgen Endal, Espen R. Jakobsen
We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of $$\partial_tu-\mathfrak{L}^{σ,μ}[φ(u)]=g(x,t)\quad\quad\text{in}…
Finite and infinite speed of propagation for porous medium equations with nonlocal pressure
Diana Stan, Félix del Teso, Juan Luis Vázquez
We study a porous medium equation with fractional potential pressure: for , and .…